Three Positive Numbers

What three positive numbers give the same result when multiplied and added together?

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September 10th, 2015 | Category: Mathematical |  Email This Riddle

8 guesses to Three Positive Numbers

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• Frank

  September 10, 2015 at 8:53 AM

  1,2,3

• anant

  September 10, 2015 at 9:08 AM

  1,2,3

• Dude

  September 11, 2015 at 9:05 AM

  Frank, you are today’s winner!
  1, 2, and 3.

• Margot

  September 11, 2015 at 10:46 PM

  1,2,3

• brent

  September 14, 2015 at 2:28 AM

  Looks like the square root of 3 would also solve this riddle if it is used as all three values.
  root 3 x root 3 x root 3 = root 3 + root 3 + root 3

  I don’t know how to tell if there are other solutions (other than the one Frank gave) where three unique values solve the problem? Any ideas?

• brent

  September 14, 2015 at 8:09 PM

  O.K. I’ve found a general solution (but my inability to enter math formulae on here is a bit frustrating, I’m happy to follow-up if there is interest.

  But for example,
  If you assume A = square root of (11.1)
  Which is approximately 3.331666

  Then this is true:
  A/10 + A + Ax10 = A/10 x A x Ax10
  or approximately
  0.3331666 + 3.331666 + 33.31666 = 0.3331666 x 3.331666 x 33.31666 = 36.98149

• brent

  September 16, 2015 at 8:25 AM

  For some reason, this one has captured me!

  Another three positive numbers that add up to their product are:
  (Where B = square root of 3.5)
  B/2 + B + 2B = B/2 x B x 2B

  Or approximately:
  0.935414 + 1.870829 + 3.741657 = 0.935414 x 1.870829 x 3.741657 = 6.5479

• brent

  September 16, 2015 at 8:38 AM

  Oh boy, it is much easier than I had been making it out to be.

  Given any two positive numbers: B & C you can find the 3rd (usually smaller) number to complete the equation:
  A + B + C = A x B x C

  using: A = (B + C) / (B x C – 1)

  Of course, B x C – 1 must not equal 0.

  I think I can get on with my life now…